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課程名稱 |
環論專題一
Topics in Ring Theory (Ⅰ) |
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開課學期 |
100-1 |
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授課對象 |
理學院 數學研究所 |
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授課教師 |
李秋坤 |
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課號 |
MATH8109 |
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課程識別碼 |
221 D1410 |
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班次 |
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學分 |
3 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期三6,7,8(13:20~16:20) |
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上課地點 |
天數304 |
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備註 |
限研究生。
總人數上限：20人 |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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課程大綱
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課程概述 |
The course contains two parts: (1) Basic theory of PI-algebras and (2) Noncrossed product division algebras.
(1)Free algebras, difference operators for polynomials
(2)PI-algebras:
Amitsur’s theorem for matrix algenbras;
Density Theorem for primitive algebras;
Kaplansky’s theorem for primitive PI-algebras
Posner’s theorem for prime PI-algebras
Central polynomials
(3)Applications to finite-dimensional algebras
Division algebras with low dimensions;
Crossed products
Brauer groups
Splitting fields for division algebrs
(4)Noncrossed product division algebras:
The construction of the first noncrossed division algebras by Amitsur.
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課程目標 |
The course is considered as basic study of both PI-algebras and finite-dimensional. division algebras. |
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課程要求 |
Ring Theory I, II |
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預期每週課後學習時數 |
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Office Hours |
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參考書目 |
(1) N. Jacobson, PI-algebras: an introduction, Lecture Notes in Mathematics 441, 1975
(2) Draxl, P. K. Skew fields. London Mathematical Society Lecture Note Series, 81. Cambridge University Press, Cambridge, 1983. ix+182 pp.
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指定閱讀 |
(1) N. Jacobson, PI-algebras: an introduction, Lecture Notes in Mathematics 441, 1975
(2) Draxl, P. K. Skew fields. London Mathematical Society Lecture Note Series, 81. Cambridge University Press, Cambridge, 1983. ix+182 pp.
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
期中 |
50% |
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2. |
期末 |
50% |
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